Today, a shopping mall is provided on a Web page on the Internet. Such a shopping mall may be a virtual three-dimensional world. A number of three-dimensional commodity objects are disposed within a virtual shop object in the shopping mall. In accordance with a virtual three-dimensional image displaying program, a server machine or a client machine may generate images in the virtual three-dimensional shopping mall for displaying. One of the objects within the virtual shopping mall may be linked to another one of the objects by means of a URL.
A conventional virtual three-dimensional image displaying program is operative to dispose objects in a virtual three-dimensional space in accordance with sets of object data representative of three-dimensional shapes and positions of the objects, and to project the objects on a two-dimensional plane in accordance with a field of view of a user in the space to thereby generate corresponding two-dimensional images. When two objects partially overlap with each other as viewed from the user's viewpoint, the images of these objects must be generated so that the overlapping portion of one object which is deeper or farther from the viewpoint hides behind the other object which is shallower or closer to the viewpoint. Meanwhile, when there is disposed a semi-transparent object, the images of the objects must be generated so that the objects behind the semi-transparent object can be seen through the semi-transparent object.
The Z buffer algorithm is typically used in order to properly process relative overlapping of objects as viewed from the viewpoint. In accordance with this algorithm, for rendering the images of objects onto a two-dimensional frame buffer memory, the objects are separated into elemental polygons, and Z-values representative of positions of a plurality of polygons of the objects relative to the viewpoint are stored in a so-called Z buffer. For rendering pixels of two or more object polygons at the same pixel locations onto the two-dimensional frame buffer memory, in accordance with the algorithm, the Z-values of the object polygons are compared with each other and only the pixels of one of the object polygons that is closest to the viewpoint are ultimately stored at the locations. For rendering an image of a semi-transparent object, a so-called alfa blending method is used to render, onto the frame buffer memory, values representative of a color of the pixels of the semi-transparent object blended with colors of the pixels of other object polygons disposed behind the semi-transparent object in accordance with the degree of the transparency of the semi-transparent object.
According to the Z buffer algorithm and the alfa blending method, for rendering the image of the semi-transparent object, the objects must be rendered in order of the distance from farther object polygons to closer object polygons relative to the viewpoint. For this purpose, before the rendering, a so-called Z sorting method is used to first determine the distances of all of the displayed object polygons from the viewpoint and then sort the object polygons in accordance with the distances.